You can browse or search the archive via the Archive page. The channels list on the right show the channels available. You can search via the form on the top left, or if you are on a mobile device, opening the menu, as well as on the form on the archive pache.
Greyed out channels are archived channels in Slack itself. You can still read the messages in there of course, but accessing it or posting new messages has been limited on Slack itself.
If you choose to do so, you can log in with Slack. This gives you the option to favourite messages, so you can easily find them again in your account here on the archive.